We discuss valley current, which is carried by quasi-particles in graphene. We show that the valley current arises owing to a peculiar term in the electron-phonon collision integral that mixes the scalar and vector gauge-field-like vertices in the electron-phonon interaction. This mixing makes collisions of phonons with electrons sensitive to their chirality, which is opposite in two valleys. As a result of collisions with phonons, electrons of the different valleys deviate in the opposite directions. The valley-dependent deviation of the quasi-particle current does not request for breaking the spatial inversion symmetry.The effect exists both in a pristine graphene or bilayer graphene samples, and it increases with temperature owing to a higher rate of collisions with phonons at higher temperatures. The valley current carried by quasi-particles could be detected by measuring electric current using a non-local transformer of a suitable design.

To appear in Ankang Liu and A. Finkel'stein, PRB Rapid Communications (2020).